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Main Title: Existence and uniqueness of solutions of stochastic functional differential equations
Author(s): Renesse, Max-K. von
Scheutzow, Michael
Type: Article
Language Code: en
Abstract: Using a variant of the Euler–Maruyama scheme for stochastic functional differential equations with bounded memory driven by Brownian motion we show that only weak one-sided local Lipschitz (or “monotonicity”) conditions are sufficient for local existence and uniqueness of strong solutions. In case of explosion the method yields the maximal solution up to the explosion time. We also provide a weak growth condition which prevents explosions to occur. In an appendix we formulate and prove four lemmas which may be of independent interest: three of them can be viewed as rather general stochastic versions of Gronwall's Lemma, the final one provides tail bounds for Hölder norms of stochastic integrals.
Issue Date: 2010
Date Available: 30-Nov-2017
DDC Class: 510 Mathematik
Subject(s): stochastic functional differential equation
existence of solution
maximal solution
uniqueness of solution
Dereich lemma
stochastic Gronwall lemma
Sponsor/Funder: DFG, FOR 718, Analysis and stochastics in complex physical systems
Journal Title: Random operators and stochastic equations
Publisher: De Gruyter
Publisher Place: Berlin [u.a.]
Volume: 18
Issue: 3
Publisher DOI: 10.1515/rose.2010.015
Page Start: 267
Page End: 284
EISSN: 1569-397X
ISSN: 0926-6364
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Stochastische Analysis » Publications

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